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The entropy of rational Powers shifts

Author(s): Geoffrey L. Price
Journal: Proc. Amer. Math. Soc. 126 (1998), 1715-1720.
MSC (1991): Primary 46L55, 46L40, 46L10
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Abstract: The Connes-Størmer entropy of all rational Powers shifts is shown to be $\frac 12\log 2$.

References:

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M. Choda, Entropy for $^*$-endomorphisms and relative entropy for subalgebras, J. Operator Theory 25 (1991), 125-140. MR 94a:46098

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A. Connes, H. Narnhofer and W. Thirring, Dynamical entropy of $C^*$-algebras and von Neumann algebras, Commun. Math. Phys. 112 (1987), 691-719. MR 89b:46078

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A. Connes and E. Størmer, Entropy for automorphisms of $\mathrm{II}_1$ von Neumann algebras, Acta Math. 134 (1975), 289-306. MR 56:12906

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V. Golodets and E. Størmer, Entropy of $C^*$-dynamical systems defined by bitstreams, Univ. of Oslo preprint, 1996.

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H. Narnhofer and W. Thirring, Chaotic properties of the non-commutative 2-shift, From Phase Transitions to Chaos, World Science Publishing, 1992, pp. 530-546. MR 93i:46119

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R. T. Powers and G. Price, Binary shifts on the hyperfinite $\mathrm{II}_1$ factor, American Mathematical Society Series in Contemporary Mathematics 145 (1993), 453-464. MR 94h:46098

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R. T. Powers and G. Price, Cocycle conjugacy classes of shifts on the hyperfinite $\mathrm{II}_1$ factor, J. Funct. Anal. 121 (1994), 275-295. MR 95g:46110

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G. Price, Shifts on the hyperfinite $\mathrm{II}_1$ factor, USNA preprint.

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Additional Information:

Geoffrey L. Price
Affiliation: Department of Mathematics 9E, United States Naval Academy, Annapolis, Maryland 21012
Email: glp@sma.usna.navy.mil

DOI: 10.1090/S0002-9939-98-04304-4
PII: S 0002-9939(98)04304-4
Keywords: Entropy, automorphisms, endomorphisms, factor, von Neumann algebras, noncommutative dynamical systems
Received by editor(s): November 19, 1996
Additional Notes: The author was supported in part by a grant from the National Security Agency and by a United States Naval Academy Recognition Grant
Communicated by: Palle E. T. Jorgensen
Copyright of article: Copyright 1998, American Mathematical Society

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